WASHINGTON—President Barack Obama on Wednesday tried to beat back criticism of one of his former top economic advisers, Lawrence Summers, from congressional Democrats who don't want to see him get the top job at the Federal Reserve.

In separate closed-door meetings with House and Senate Democrats, the president made clear he hasn't decided on a nominee to succeed Ben Bernanke as central bank chairman, according to lawmakers at the meetings. He told them he had interviewed several people, indicating he is considering...